In this paper, after the introduction of the basic concepts and the main results on K〓 theory, relative K〓 theory and the theory of classical groups of degree 2 which is related to K〓 theory, we study the problems of the computation of K〓 for the ring of integers of quadratic imaginary fields, examples of subrings of quadratic fields which are not universal for GE〓 and generating set of the Cokernel of the canonical homomorphism from K〓 to K〓.
本文在介绍了K〓理论和相对K〓理论以及与K〓理论有关的2阶典型群的基本概念及主要成果之后，对于虚二次域代数整环的K〓群的计算，非GE〓泛的虚二次域的子环以及K〓到K〓的自然同态的余核的生成元集等问题进行了研究。
This course, which discusses elementary of computational number theory, includes the following subjects:(1) Fundamental properties of Integers; (2) Congruences; (3) Congruent equations; (4) Legendre and Jacobi symbols; (5) Primitive roots; (6) Primality testing and factorization; (7) Index computation and discrete logarithm computation; (8) Other computational problems.
本课程将讨论计算数论的基本知识，主要包括以下内容：(1)整数基本性质；(2)同余；(3)同余式；(4) Legendre和Jacobi符号；(5)原根；(6)素性测试和大数分解；(7)指数计算和离散对数计算；(8)其他计算问题。
The deeper properties of integers are studied in number theory, from which come such popular results as Fermat's Last Theorem.
在数论中更深入的研究整数性质，通俗的成果例如费马大定理就是在数论中产生的。
According to algebraic number theory, all solutions of Pocklington equation in a ring of integers of a quadratic imaginary field are determined, which implies that the equation has only several solutions in the ring.
利用代数数论的理论与方法，决定了一个重要的不定方程在一个特殊的虚二次域整数环中的解，从而指出这个方程在比整数环更大的环中也仅有有限个解。
RSA is a successful public-key cryptography algorithm in theory and application, the core operation of RSA is performing modular exponentiation with very long integers, nowadays, the safe length of RSA key is 1024 bits, which recognized by international.
RSA算法是目前理论与应用上均比较成功的公钥密码算法，其核心运算是大数模幂运算，当前，国际公认的RSA算法密钥的安全长度为1024位。
The logical basis for the theory of the integers that Euclid presented in Books VII to IX of the " Elements " was woefully deficient.
欧几里德在《原本》的第七到第九册中提出的整数理论的逻辑基础是十分令人遗憾地有缺陷的。